Members = 1,000*3^t where t = months
So after
0 months 1,000 members
1 month 3,000 members
2 months 9,000 members
If we are to solve that for a million:
Members/1,000 = 3^t
1,000,000/1,000 = 3^t
1,000 = 3^t
Taking logs of both sides
log 1,000 = time*log(3)
3 = time * 0.4771212547
time = 3/ 0.4771212547
time = 6.2877098229 months
Okay about 6.29 months